\documentclass[border=.1cm]{standalone}
\usepackage{tikz}
\usepackage{times}
\usepackage{pgfplots}

\begin{document}

\pgfdeclarelayer{background layer}
\pgfdeclarelayer{foreground layer}
\pgfsetlayers{background layer,main,foreground layer}

\begin{tikzpicture}

\begin{scope}[x={(.91cm,.2cm)},y={(0cm,1cm)},z={(.4cm,-.2cm)}]

\pgfmathsetmacro{\os}{5}

\begin{scope}[every path/.style={thick}]

\draw (0,1,0) circle (1cm);
\draw[gray,dashed](0,1,0) ellipse(1cm and .15cm);

\begin{scope}[xshift=\os cm]

\begin{pgfonlayer}{foreground layer}
\draw[shift={+(0,0,.5)}] (0,0,0) -- (-.577, .577, .577);
\draw[shift={+(0,0,.5)}] (0,0,0) -- (-.577,-.577, .577);
\draw[shift={+(0,0,.5)}] (0,0,0) -- ( .577,-.577, .577);
\draw[shift={+(0,0,.5)}] (0,0,0) -- ( .577, .577, .577);
\draw[shift={+(0,0,.5)},fill=white] (-.577,.577,.577) \foreach \t in {145,155,...,215} {--({cos(\t)*cos(45)},{sin(\t)},{-cos(\t)*sin(45)})};
\draw[shift={+(0,0,.5)},fill=white] (.577,.577,.577)  \foreach \t in {145,155,...,215} {--({cos(\t)*cos(135)},{sin(\t)},{-cos(\t)*sin(135)})};
\draw[shift={+(0,0,.5)},fill=white] (.577,.577,.577)  \foreach \t in {145,155,...,215} {--({sin(\t)},{cos(\t)*cos(135)},{-cos(\t)*sin(135)})};
\draw[shift={+(0,0,.5)},fill=white] (.577,-.577, .577) \foreach \t in {145,155,...,215} {--({sin(\t)},{cos(\t)*cos(45)},{-cos(\t)*sin(45)})};
\fill[white,shift={+(0,0,.5)}] (-.577, .577, .577) -- (-.577,-.577, .577) -- (.577,-.577, .577) -- (.577, .577, .577) -- cycle;
\end{pgfonlayer}

\begin{pgfonlayer}{background layer}
\draw[shift={+(0,0,-.5)}] (0,0,0) -- (-.577, .577,-.577);
\draw[shift={+(0,0,-.5)}] (0,0,0) -- (-.4,-.577,-.577);
\draw[shift={+(0,0,-.5)}] (0,0,0) -- ( .577,-.577,-.577);
\draw[shift={+(0,0,-.5)}] (0,0,0) -- ( .577, .577,-.577);
\draw[shift={+(0,0,-.5)}] (-.577,.577,-.577) \foreach \t in {145,150,...,160} {--({cos(\t)*cos(45)},{sin(\t)},{cos(\t)*sin(45)})};
\draw[shift={+(0,0,-.5)}] (.577,.577,-.577)  \foreach \t in {145,155,...,215} {--({cos(\t)*cos(135)},{sin(\t)},{cos(\t)*sin(135)})};
\draw[shift={+(0,0,-.5)}] (-.577,.577,-.577)  \foreach \t in {215,210,...,185} {--({sin(\t)},{cos(\t)*cos(135)},{cos(\t)*sin(135)})};
\draw[shift={+(0,0,-.5)}] (.577,-.577, -.577) \foreach \t in {145,155,...,200} {--({sin(\t)},{cos(\t)*cos(45)},{cos(\t)*sin(45)})};
\end{pgfonlayer}

\draw[shift={+(.5,0,0)}] (0,0,0) -- ( .577, .577,-.577);
\draw[shift={+(.5,0,0)}] (0,0,0) -- ( .577,-.577,-.577);
\draw[shift={+(.5,0,0)}] (0,0,0) -- ( .577,-.577, .577);
\draw[shift={+(.5,0,0)}] (0,0,0) -- ( .577, .577, .577);
%\draw[shift={+(.5,0,0)}] ( .577,.577,-.577) \foreach \t in {145,155,...,215} {--({-cos(\t)*sin(45)},{sin(\t)},{cos(\t)*cos(45)})};
\draw[shift={+(.5,0,0)}] (.577,.577,.577)  \foreach \t in {145,155,...,215} {--({-cos(\t)*sin(135)},{sin(\t)},{cos(\t)*cos(135)})};
\draw[shift={+(.5,0,0)}] (.577,.577,.577)  \foreach \t in {145,155,...,215} {--({-cos(\t)*sin(135)},{cos(\t)*cos(135)},{sin(\t)})};
\draw[shift={+(.5,0,0)}] (.577,-.577, .577) \foreach \t in {145,155,...,215} {--({-cos(\t)*sin(45)},{cos(\t)*cos(45)},{sin(\t)})};

\begin{pgfonlayer}{foreground layer}
%\draw[shift={+(-.5,0,0)}] (0,0,0) -- (-.577, .577,-.577);
%\draw[shift={+(-.5,0,0)}] (0,0,0) -- (-.577,-.577,-.577);
\draw[shift={+(-.5,0,0)}] (0,0,0) -- (-.577,-.577, .577);
\draw[shift={+(-.5,0,0)}] (0,0,0) -- (-.577, .577, .577);
\draw[shift={+(-.5,0,0)},fill=white] (-.577,.577,-.577) \foreach \t in {145,155,...,215} {--({cos(\t)*sin(45)},{sin(\t)},{cos(\t)*cos(45)})};
\draw[shift={+(-.5,0,0)},fill=white] (-.577,.577,.577)  \foreach \t in {145,155,...,215} {--({cos(\t)*sin(135)},{sin(\t)},{cos(\t)*cos(135)})};
\draw[shift={+(-.5,0,0)},fill=white] (-.577,.577,.577)  \foreach \t in {145,155,...,215} {--({cos(\t)*sin(135)},{cos(\t)*cos(135)},{sin(\t)})};
\draw[shift={+(-.5,0,0)},fill=white] (-.577,-.577, .577) \foreach \t in {145,155,...,215} {--({cos(\t)*sin(45)},{cos(\t)*cos(45)},{sin(\t)})};
\fill[white,shift={+(-.5,0,0)}] (0,0,0) -- (-.577,-.577,.577) -- (-.577,.577,.577) -- cycle;
\end{pgfonlayer}

\begin{pgfonlayer}{foreground layer}
%\draw[shift={+(0,.5,0)}] (0,0,0) -- ( .577, .577,-.577);
\draw[shift={+(0,.5,0)}] (0,0,0) -- (-.577, .577,-.577);
\draw[shift={+(0,.5,0)}] (0,0,0) -- (-.577, .577, .577);
\draw[shift={+(0,.5,0)}] (0,0,0) -- ( .577, .577, .577);
\draw[shift={+(0,.5,0)},fill=white] ( .577,.577,-.577) \foreach \t in {145,155,...,215} {--({sin(\t)},{-cos(\t)*sin(45)},{cos(\t)*cos(45)})};
\draw[shift={+(0,.5,0)},fill=white] (.577,.577,.577)  \foreach \t in {145,155,...,215} {--({sin(\t)},{-cos(\t)*sin(135)},{cos(\t)*cos(135)})};
\draw[shift={+(0,.5,0)},fill=white] (.577,.577,.577)  \foreach \t in {145,155,...,215} {--({cos(\t)*cos(135)},{-cos(\t)*sin(135)},{sin(\t)})};
\draw[shift={+(0,.5,0)},fill=white] (-.577,.577, .577) \foreach \t in {145,155,...,215} {--({cos(\t)*cos(45)},{-cos(\t)*sin(45)},{sin(\t)})};
\fill[white,shift={+(0,.5,0)}] (0,0,0) -- (-.577,.577,.577) -- (.577,.577,.577) -- cycle;
\end{pgfonlayer}

\begin{pgfonlayer}{background layer}
\draw[shift={+(0,-.5,0)}] (0,0,0) -- ( .577,-.577,-.577);
\draw[shift={+(0,-.5,0)}] (0,0,0) -- (-.577,-.577,-.577);
\draw[shift={+(0,-.5,0)}] (0,0,0) -- (-.577,-.577, .577);
\draw[shift={+(0,-.5,0)}] (0,0,0) -- ( .577,-.577, .577);
%\draw[shift={+(0,-.5,0)}] ( .577,-.577,-.577) \foreach \t in {145,155,...,215} {--({sin(\t)},{cos(\t)*sin(45)},{cos(\t)*cos(45)})};
\draw[shift={+(0,-.5,0)}] (.577,-.577,.577)  \foreach \t in {145,155,...,215} {--({sin(\t)},{cos(\t)*sin(135)},{cos(\t)*cos(135)})};
%\draw[shift={+(0,-.5,0)}] (.577,-.577,.577)  \foreach \t in {145,155,...,215} {--({cos(\t)*cos(135)},{cos(\t)*sin(135)},{sin(\t)})};
\draw[shift={+(0,-.5,0)}] (-.577,-.577, .577) \foreach \t in {145,155,...,215} {--({cos(\t)*cos(45)},{cos(\t)*sin(45)},{sin(\t)})};
\end{pgfonlayer}

\draw [-stealth](0,1.5,0) -- (0,2.5,0);
\node at (0,3.,0){\tt ORIENTATION(1:3,6)=0,0,1};
\draw [-stealth](0,-1.5,0) -- (0,-2.5,0);
\node at (0,-3.,0){\tt ORIENTATION(1:3,5)=0,0,-1};

\draw [-stealth](1.5,0,0) -- (2.5,0,0);
\node at (4.2,.2,0){\tt ORIENTATION(1:3,2)=1,0,0};
\draw [-stealth](-1.5,0,0) -- (-2.5,0,0);
\node at (-4.2,-.2,0){\tt ORIENTATION(1:3,1)=-1,0,0};

\begin{pgfonlayer}{foreground layer}
\draw [-stealth](0,0,1.5) -- (0,0,2.5);
\node at (2.5,-1,2.5){\tt ORIENTATION(1:3,3)=0,-1,0};
\end{pgfonlayer}

\end{scope}

\end{scope}
\end{scope}

\end{tikzpicture}
\end{document}
